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dc.contributor.authorPeyre, Gabriel
dc.contributor.authorCuturi, Marco
dc.contributor.authorSolomon, Justin
dc.date.accessioned2017-12-21T14:48:51Z
dc.date.available2017-12-21T14:48:51Z
dc.date.issued2016-06
dc.identifier.urihttp://hdl.handle.net/1721.1/112918
dc.description.abstractThis paper presents a new technique for computing the barycenter of a set of distance or kernel matrices. These matrices, which define the interrelationships between points sampled from individual domains, are not required to have the same size or to be in row-by-row correspondence. We compare these matrices using the softassign criterion, which measures the minimum distortion induced by a probabilistic map from the rows of one similarity matrix to the rows of another; this criterion amounts to a regularized version of the Gromov-Wasserstein (GW) distance between metric-measure spaces. The barycenter is then defined as a Fréchet mean of the input matrices with respect to this criterion, minimizing a weighted sum of softassign values. We provide a fast iterative algorithm for the resulting nonconvex optimization problem, built upon state-of-the-art tools for regularized optimal transportation. We demonstrate its application to the computation of shape barycenters and to the prediction of energy levels from molecular configurations in quantum chemistry.en_US
dc.description.sponsorshipNational Science Foundation (U.S.) (Mathematical Sciences Postdoctoral Research Fellowship Award 1502435)en_US
dc.language.isoen_US
dc.publisherAssociation for Computing Machineryen_US
dc.relation.isversionofhttp://dl.acm.org/citation.cfm?id=3045671en_US
dc.rightsCreative Commons Attribution-Noncommercial-Share Alikeen_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/4.0/en_US
dc.sourceMIT Web Domainen_US
dc.titleGromov-wasserstein averaging of kernel and distance matricesen_US
dc.typeArticleen_US
dc.identifier.citationPeyre, Gabriel, Marco Cuturi and Justin Solomon. "Gromov-wasserstein averaging of kernel and distance matrices." Proceedings of the 33rd International Conference on International Conference on Machine Learning ICML'16, New York, NY, 19-24 June, 2016. Vol. 48, Association for Computing Machinery, 2016. pp. 2664-2672.en_US
dc.contributor.departmentMassachusetts Institute of Technology. Department of Electrical Engineering and Computer Scienceen_US
dc.contributor.mitauthorSolomon, Justin
dc.relation.journalProceedings of the 33rd International Conference on International Conference on Machine Learningen_US
dc.eprint.versionAuthor's final manuscripten_US
dc.type.urihttp://purl.org/eprint/type/ConferencePaperen_US
eprint.statushttp://purl.org/eprint/status/NonPeerRevieweden_US
dspace.orderedauthorsPeyre, Gabriel; Cuturi, Marco; Solomon, Justinen_US
dspace.embargo.termsNen_US
mit.licenseOPEN_ACCESS_POLICYen_US
mit.metadata.statusComplete


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